Bearing Units
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Antec 120mm SmartCool Fan Unit Double Ball Bearing (Variable Speed) List Price: $30.99 Sale Price: $11.99 Average Rating:   |
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The thermally-controlled Antec 120mm SmartCool case fan is up to 80% quieter than other fans. Its RPM increases as the temperature rises inside of the case. It features a double ball-bearing design for extended life... |
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A steel ball bearing is 7 cm in diameter at 30◦C.?
A steel ball bearing is 7 cm in diameter at
30◦C. A bronze plate has a hole in it that is
6.994 cm in diameter at 30◦C.
What common temperature must they have
in order that the ball just squeeze through the
hole?
Answer in units of ◦C.
Please help. I don't get it...
As the metals heat up, they expand. The bronze plate expands, making the hole bigger, but steel ball will also get bigger. The amount that they expand depends on a characterstic value called the "coefficient of linear expansion". It is about 13E-6/K for steel and about 18E-6/K for bronze. Since the bronze number is more than steel, it the ring will grow faster than the ball as the temperature rises. At some point, the hole size will "catch up" to the ball size.
Use the equation L1 = L0 (1 + a(T1-T0)),
where L1 is the resulting length, L0 is the starting length, a is the coefficient, and T1-T0 is the change in temperature.
For bronze L1 = 6.994(1 + 18E-6(T-30)),
for steel L1 = 7.0(1 + 13E-6(T-30).
Set the equal and solve for T
6.994(1 + 18E-6(T-30)) = 7.0(1 + 13E-6(T-30).
I think it occurs at 1230 degrees; but double check the solution.